Pour white vinegar into a spray bottle.
Saturate the shower door with the vinegar and let it set for 15 to 20 minutes. Spray the doors every few minutes to keep it damp.
Dampen a sponge with warm water and sprinkle baking soda on it.
Scrub the shower doors with the sponge. The baking soda acts as a mild abrasive to lift stubborn soap stains.
Rinse the door with warm water to remove the soap scum and baking soda.
Squeegee the doors from top to bottom to eliminate the excess moisture.
Repeat the process if necessary until the stains are gone.